Game Development Reference
In-Depth Information
CHAPTER 1
Basic Concepts
As a warm-up, this chapter will cover the most basic of the principles that will be used
and referenced throughout the remainder of this topic. First, we'll introduce Newton's
laws of motion, which are very important in the study of mechanics. Then we'll discuss
units and measures, where we'll explain the importance of keeping track of units in your
calculations. You'll also have a look at the units associated with various physical quan‐
tities that you'll be studying. After discussing units, we'll define our general coordinate
system, which will serve as our standard frame of reference. Then we'll explain the
concepts of mass, center of mass, and moment of inertia, and show you how to calculate
these quantities for a collection, or combination, of masses. Finally, we'll discuss New‐
ton's second law of motion in greater detail, take a quick look at vectors, and briefly
discuss relativistic time.
Newton's Laws of Motion
In the late 1600s (around 1687), Sir Isaac Newton put forth his philosophies on me‐
chanics in his Philosophiae Naturalis Principia Mathematica . In this work Newton sta‐
ted the now-famous laws of motion, which are summarized here:
Law I
A body tends to remain at rest or continue to move in a straight line at constant
velocity unless acted upon by an external force. This is the so-called concept of
inertia.
Law II
The acceleration of a body is proportional to the resultant force acting on the body,
and this acceleration is in the same direction as the resultant force.
Law III
For every force acting on a body (action) there is an equal and opposite reacting
force (reaction), where the reaction is collinear to the acting force.